London: Physicists claim to have developed a simple equation that explains and predicts the shape of a ponytail, a finding they say could help scientists better understand natural materials such as wool and fur.

The new equation, the researchers said, also takes into account the stiffness of hair, the effects of gravity and the presence of random curliness or waviness.

The work, published in Physical Review Letters journal, could help scientists better understand natural materials, such as wool and fur.

According to the physicist, their findings showed how physics could be used to "solve a problem that has puzzled scientists and artists ever since Leonardo da Vinci remarked on the fluid-like streamlines of hair in his notebooks 500 years ago".

Prof Goldstein worked on the equation with Prof Robin Ball from the University of Warwick and Patrick Warren, from Unilever's Research and Development Centre.

The "Ponytail Shape Equation", they said, represents the first scientific understanding of the distribution of hair in a ponytail.

It provides new understanding of how a bundle is swelled by the outward pressure which arises from collisions between the component hair, they noted.

Together with a new mathematical quantity known as the Rapunzel Number, the equation can be used to predict the shape of any ponytail, they explained.

It opens the way to a better understanding of materials made up of random fibres. This will resonate with some in the computer graphics and animation industry, where a realistic representation of hair and fur has proven a tough challenge, the researchers added.

The research will be presented at an upcoming meeting of the American Physical Society in Boston later this month. (Agencies)